What is the integral of 2sin(x)\sqrt[3]{1+cos(x)} ?

The integral of 2sin(x)\sqrt[3]{1+cos(x)} is -3/2 (1+cos(x))^{4/3}+C

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integral of 2sin(x)\sqrt[3]{1+cos(x)}

- \frac{3}{2} (1 + cos (x))^{\frac{4}{3}} + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply u-substitution

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= 2 (- \frac{3}{4} u^{\frac{4}{3}})

Substitute back

u = 1 + cos (x)

= 2 (- \frac{3}{4} (1 + cos (x))^{\frac{4}{3}})

Simplify

2 (- \frac{3}{4} (1 + cos (x))^{\frac{4}{3}}) : - \frac{3}{2} (1 + cos (x))^{\frac{4}{3}}

= - \frac{3}{2} (1 + cos (x))^{\frac{4}{3}}

Add a constant to the solution

= - \frac{3}{2} (1 + cos (x))^{\frac{4}{3}} + C

\frac{d}{d x} (\frac{x ^{3} - 2 x x}{x})

(0, - 9), (7, 6)

f (x) = x (x^{2} - 4 x + 5)^{5}, at x = 2

x \cdot y^{^{'}} = 2 y + e^{x} \cdot x^{3}

x \to - \frac{1}{2} lim (\frac{7}{2 x + 1})

What is the integral of 2sin(x)\sqrt[3]{1+cos(x)} ?
The integral of 2sin(x)\sqrt[3]{1+cos(x)} is -3/2 (1+cos(x))^{4/3}+C